k-step nilpotent Lie algebras

Author:

Goze Michel,Remm Elisabeth

Abstract

AbstractThe classification of complex or real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example, the nilpotent Lie algebras are classified only up to dimension 7. Moreover, to recognize a given Lie algebra in the classification list is not so easy. In this work, we propose a different approach to this problem. We determine families for some fixed invariants and the classification follows by a deformation process or a contraction process. We focus on the case of 2- and 3-step nilpotent Lie algebras. We describe in both cases a deformation cohomology for this type of algebras and the algebras which are rigid with respect to this cohomology. Other

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Cited by 15 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Deformations and rigidity in varieties of Lie algebras;Journal of Pure and Applied Algebra;2023-03

2. Nilpotent Lie algebras of class 3 with 1-dimensional center and 3-dimensional derived subalgebra;Communications in Algebra;2022-04-23

3. Generalized deformation of complex structures on nilmanifolds;Differential Geometry and its Applications;2021-10

4. On rigid 2-step nilpotent Lie superalgebras;Communications in Algebra;2021-01-08

5. Degenerations of graph Lie algebras;Linear and Multilinear Algebra;2020-01-13

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